Global well-posedness of the Cauchy problem of two-dimensional compressible Navier-Stokes equations in weighted spaces

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:255

Article

Jiu, Quansen^1,3  Wang, Yi^2,3  Xin, Zhouping³ 

[1] Capital Normal Univ, Sch Math Sci, Beijing 100048, Peoples R China

[2] Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100190, Peoples R China

[3] Chinese Univ Hong Kong, Inst Math Sci, Hong Kong, Hong Kong, Peoples R China

关键词: Compressible Navier-Stokes equations;    Density-dependent viscosity;    Global well-posedness;    Vacuum;    Weighted estimates;   

DOI  :  10.1016/j.jde.2013.04.014

来源: Elsevier

【 摘 要 】

In this paper, we study the global well-posedness of classical solution to 2D Cauchy problem of the compressible Navier-Stokes equations with large initial data and vacuum. It is proved that if the shear viscosity mu. is a positive constant and the bulk viscosity lambda is the power function of the density, that is, lambda(rho) = rho(beta) with beta > 3, then the 2D Cauchy problem of the compressible Navier-Stokes equations on the whole space R-2 admits a unique global classical solution (rho, u) which may contain vacuums in an open set of R-2. Note that the initial data can be arbitrarily large to contain vacuum states. Various weighted estimates of the density and velocity are obtained in this paper and these self-contained estimates reflect the fact that the weighted density and weighted velocity propagate along with the flow. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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